Plane strain head-scratcher. Engineering brain-power needed.

I stretch them to a certain strain.

If the poymers are the same and the strain in the tape is the same I would expect the change in thickness to be the same.

Are you sure you are stretching them to the same strain and not just the same load or distance?

Del,

I'm positive the strain is the same in my experimental setup. The test is done in a tensile tester, all the samples have the same starting lentgh and I've programmed the machine to stop after a certain travelling distance has been reached. Then from the definition of engineering strain, they're all the same.

Then again, if you want to try and compare true strains defined by the change in area things start to look different. The true strain in the area does not give me the same true strain as the true strain calculated from the lentgh, which makes things look even more ackward. From the traditional mechanics point of view, this is dogdgy since they are supposed to be one and the same but the difference between them is much larger than the error that could be carried from the measurements.

all the samples have the same starting lentgh and I've programmed the machine to stop after a certain travelling distance has been reached.

My A level physics is a bit shaky so I'm not sure if that gives the same strain.

Maybe someone else can help out...I don't feel like checking all that elongation/stress/strain stuff. Hopefully this extra info' will help.

Hello, I have sold tapes for about a decade and the surface area of the wider tape is greater; therefore, the stress test is going to have different results. The wider tape's thickness will not reduce at the same rate as the narrow one because the wider tape can with stand a higher stress and load rating than the narrower width tape.

I hope this helps.

Mr. Tapes

Mr Tapes,

The area is larger and that makes the tape withstand a higher load, but not a higher stress being the stress defined as the load by cross-sectional area. The stress ends up being the same. Of course when the tape is streched, the crossectional area is reduced and the macromolecules are aligned which increases the young's modulus and ergo the true stress in the tape. But that is not what I'm concerned with.

The test is being done at a constant strain rate [x.xx mm/min] and stop after x mm (I just let the tensile tester read the load from the load cell and save it for me). At then end of the day what matters is not the forces registered or the stresses involved but the final geometry which my question was aimed at.

The wide tape does seem to suffer a quicker reduction in thickness than in width when compared to the narrow tape (when both starting thicknesses were equal). This is purely a geometrical issue but I cannot find a reasonable mechanics/geometry explanation to it and I was hoping somebody could cook something up.

First, I should say that I have no experience or knowledge in this area so please feel free to ignore me.

Try thinking about taking things to silly limits. If your tape had a square cross section to begin with then you'd expect it to have a square cross section after stretching it. If the tape was very wide, you'd expect it to be nearly as wide after stretching it. Your narrow tape probably acts a (little) bit more like the former, and, your wider tape (a little) more like the latter.

Mmmmm.... that sounds very interesting indeed, but why does the wider tape stay wide after deformation?

The edges are stretched more than the middle. I was thinking "very wide". If the "end effect" is not significant then maybe the opposite effect occurs: a flat slab of blue tack stretched out would eventually form a circular cross section in the middle.

Also there may be a different "end effect": maybe the end sections don't stretch as much as the middle, and this effect has sort of positive feed back: i.e. the more the middle stretches the weaker it becomes so the more it stretches.

As I said before don't take my comments too seriously: I have no idea of the properties of polymer tape.

Here is my guess as to what is happening.

I am assuming the lengths of the wide and narrow tapes are the same. If you increase the length by a certain ratio, both the thickness and the width will reduce. I'm thinking the wider tape doesn't reduce in width as much as the narrow tape, so it reduces more in thickness.

Another way to look at it is that as it narrows down in width, there is stress across the width of the tape, pulling it inward. Because of the geometry (width to length ratio), the wider tape cannot reduce its width as much, so there is more of this crosswise stress in the wide tape, and the thickness is reduced more.

Think in terms of volumetric strain??

Thanks all for your help.

I think I'm going to try some hands on approach in FEA and then let you know what it was actually happening.

Good luck finding the right material model.